pre lab demos

2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible

website, in whole or in part. .

E X P E R I M E N T 1

For Instructors

An added feature to the eighth edition of Physics Laboratory Experiments is a set of pre-lab

Students often come to the laboratory unenthuastic. If something attention-getting (a demo)

is presented initially that is related to the lab experiment, or some other physics principle

that has been studied in class, interest is aroused. This being done, the instructor can lead

into the current lab experiment.

A list of the demonstrations follows. They are instructive and economical, usually done

with available materials and items. In some demonstrations, students can participate, adding

to the attention-getting. Enjoy.

Skewed Balloon (And it doesn't burst!)

Problem in Data Analysis (There's a dollar missing)

Mixed Liquids Become More Dense

Problem in Math Analysis (Can 2 = 1?)

Apparent Weightlessness (Where's the water?)

Different Distances of Fall (Listen to the sound)

Problem in Kinematics

Which Way Does the Bubble Go? (Mass and inertia)

-and-out)

Pendulum and Peg

Bucket Swing (What keeps the water in the pail?)

Two Ball Bounce (Energy transfer)

The Slinky Slinky (Why doesn't it fall?)

Which Way Does the Yo-yo Roll? (Torque - rotational motion)

D E M O N S T R A T I O N S

N S

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2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Candle Seesaw (Torque - equilibrium)

Too Weak to Pick It Up? (Center of gravity - equilibrium)

Stack Them Up (Center of mass - equilibrium)

Cylinder Derby (Rotational motion - moment of inertia)

Egg Spin (Rigid-body rotation)

Transverse and Longitudinal Waves (Vibrating and singing rod)

Musical Straws (Make your own kind of music)

Singing Wine Glass (Resonance)

Whirly Tube (Bloogle resonator)

Burning Dollar Bill (Money to burn)

Drinking Bird Engine (Perpetual motion?)

Salt and Ice (Melting and freezing)

Take the Heat (Specific heat)

Poke a Hole (And no leaks)

Electrostatics in Action (Levitation)

Magnetism through the Hand

Is Money Magnetic? (2 demos)

Eating Magnetic Iron for Breakfast (2 demos)

Which Rod is Magnetic?

Mirror Right -left Reversal and Nonreversal (2 demos)

Spherical Mirrors (Upside down and right-side up)

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Instructor Demonstrations

EXPERIMENT 1 . THE SCIENTIFIC METHOD AND THOUGHT

Skewed Balloon (And it doesn't burst)

The purpose of the demonstration is to get the students to think and apply the scientific

method (or scientific thinking) in forming explanations and drawing conclusions. The

demonstration consists of pushing a wooden (bamboo) skewer completely through an

Items needed

Latex rubber balloons (12-in. size)

Bamboo skewers (12-in. long, found in the grilling or cooking section)

Cooking oil (small amount)

Procedure

1. Blow up balloon to nearly full size and let air out so about 2/3 in size (about 9

inches). Tie a knot in the end to keep the balloon inflated. Note the thick areas of

the inflated balloon near the tied knot and opposite end.

2. Fully rub cooking oil on the length of the skewer with the fingers. (You can do this

openly or surreptitiously, depending on how difficult you want to make the demo

explanation.)

3. Place the sharp end of the skewer on the thick end of the balloon near the tie aiming

toward the opposite thick end. Use gentle pressure (twisting may help) and puncture

the balloon.

4. Push the skewer steadily toward the opposite end until the tip of the skewer touches

the thick end portion of the balloon. Keep pushing until the skewer tip penetrates

through the rubber a couple inches. The skewed balloon should remain inflated. (A

little air may be lost.)

5. Ask the students to explain. You may want to repeat the demonstration showing the

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Explanation

Latex rubber is made up of long-chain polymer molecules. When the balloon is punctured,

the long chains form a seal around the skewer. The cooking oil acts as a lubricant for the

puncture.

EXPERIEMENT 2. EXPERIMENTAL UNCERTAINTY (ERROR) AND

DATA ANALYSIS

Problem in Data Analysis (There's something missing)

Procedure

To illustrate a problem in data analysis, have the students consider the following:

A student wants to buy a new cell phone for $97 and borrows $50 from each of two

friends. He buys the phone and gets $3 back. He gives each friend $1 and keeps the

other $1.

Now he owes his two friends $49 apiece. But $49 plus $49 is $98; and when you add

the $1 he kept, you get $99. Where is the missing dollar?

Explanation.

The data was manipulated and the wrong figures added. The student now has a $97 cell

phone plus $1 cash. That totals $98, which indeed is what he owes to his friends.

EXPERIMENT 3. MEA SUREMENT INSTRUMENTS (MASS, VOLUME,

AND DENSITY)

Mixed Liquids Become More Dense

The purpose of this demonstration is to show the students how unexpected results may

al = 0.790

g/cm3

w = 1.000 g/cm3) are weighed (in grams), from which the

density of a mixture may be theoretically determined. The liquids are mixed, and the

the mixture is calculated and found to be greater than theoretically predicted.

5


Items Needed

Two 500 mL graduated cylinders

One 1000 ml graduated cylinder

500 mL each of methyl alcohol 95-100 % or 190-200 proof) and distilled water

(Note: Also works with ethyl alcohol, but methyl has bigger effect.)

Eye dropper

Electronic scale with tare

Procedure

1. Place one 500 mL cylinder on scale and tare.

2. Add 500 mL of methyl alcohol. (Use eye dropper to get accurate meniscus.)

3. Record mass in grams.

4. Repeat with other cylinder and 500 mL of water.

5. Place 1000 mL cylinder on scale and tare.

6. Carefully pour alcohol and water into larger cylinder.

7. Record mass and note and record the volume of the mixture.

8. Compute the density of mixture from experimental values and compare with

theoretical value. (Recall that 1 mL and 1 cm3 are equal volumes.) The experimental

density should be greater because the combined volume of the liquids is less that

1000 mL! What is going on? (Note: 500 mL of the liquids gives about a 3%

reduction in volume. Smaller volumes may be used, but the effect is more difficult

to see.)

(Note: to speed things up, the densities of methyl alcohol and water may be used to

calculate the masses in the 500 mL volumes.)

Explanation

The result should make the student aware that something hidden is going on here.

Conservation of mass applies, but why the decrease in volume? This arises because both

liquids are polar, with polar molecules having slightly electric positive and negative ends.

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As such, they form particular intermolecular lattices on the basis of charge and hydrogen

bonding. The lattices create spaces between the molecules.

When polar liquids are mixed, it is possible that the lattices pack together more closely,

taking up less space. The mixture of two liquids can therefore take up less volume than the

two liquids separately. (Lattice formation comes into play in the freezing of water. Because

of the lattice structure of ice, it is less dense that liquid water and floats.)

(Mixture results for alcohols: methyl, 960 965 mL. ethyl, 980 985 mL)

EXPERIMENT 4. SIMPLE PENDULUM PARAMETERS

Problem in Math Analysis (Can 2 = 1?)

In this experiment, there is some mathematical analysis. Emphasize to the students that an

equation is a balanced statement, numerically equal on each side of the equal sign. And as

long as the same operation is done to each side of the equation (addition, multiplication,

etc.), it is still balanced.

Procedure

Let:

x = y

Multiply by x:

x2 = xy

Multiply by y2:

x2 y

2 = xy y

2

Factor:

(x +y)(x y) = y(x y)

Divide both sides by (x y):

(x +y ) = y

But, x = y, so

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(y + y) = y

and

2y = y

Then, cancelling the y

2 = 1!

Explanation

Dividing by (x y) is dividing by zero, which is undefined.

EXPERIMENT 5. UNIFORMLY ACCELERATED MOTION

Apparent Weightlessness (Where's the water?)

Water flows freely out of two holes in a plastic cup filled with water. Yet, when the cup is

dropped, the water ceases to flow.

Items needed

Styrofoam or paper cups. (Poke holes near the bottom of the cup on opposite sides with a

pencil or other pointed object. It is helpful to prepare several cups, so the demo may be

repeated.)

Procedure

1. Fill the cup with water until continuous, thin streams of water come from the holes.

Using your fingers to cover the holes, carefully stand on a chair or lab table.

2. Hold the cup out and allow streams of water to flow from the holes. Then, quickly

drop the cup and note what happens to the streams while the cup is falling. (This is

best done over a sink or waste basket for obvious reasons.)

3. During the fall, the streams cease to flow. Ask the students why.

Explanation

As the cup falls due to gravity, the water inside the cup accelerates at the same rate and

does not come out the holes.

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Different Distances of Fall (Listen to the sound)

The purpose of this demonstration is to illustrate how uniformly accelerated motion gives

rise to different distances of fall. This is done by observing the time differences of sounds

from spaced weights that are dropped and hit a pan.

Items Needed

Cotton string

Magic marker

Weights (15 - 20)*

Pan (metal pie pan or cookie tray)

Scissors or knife (to cut string)

A couple small strips of (duct) tape

*Weights may be small metal nuts, or better yet, split-shot fishing sinkers. The latter may

be applied more accurately and easily held at a marked location.

Preparation

Cut two 3- -cm from one end of each.

String A: from the zero mark, make marks at 10 cm, 40 cm, 90 cm, 1.6 m, and 2.5 m

from the mark and attach weights at these marks.

String B: from the zero mark, make marks at 20 cm, 40 cm, 60 cm, 80 cm, 1.0 m,

1.2 m, 1.4 m, and 1.6 m and attach weights to these marks.

Procedure

1. Attach the zero mark of String A to the pan with tape and place on the floor. Stretch

out the string and have someone hold the other end while (carefully) standing on a

stool or lab table. When still and vertical, drop the string and observe the differences

in the sound made with the weights hitting the pan. (You may do this again to better

observe the times between sounds. It is helpful to have students write down what

they observe.)

2. Repeat procedure 1 using String B.

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3. Have the students explain the differences in the sounds in terms of the motions of

the weights.

(Note: You may initially show the weight distances to the students and ask them to predict

what will occur.)

Explanation

If you label the weights from the bottom as y1, y2

that there are equal time intervals between the weights hitting the pan. This may be seen

from yi = gt2, with t1, t2 = 2t1, t3 = 3t1, etc. That is, y1 = gt1

2 = 10 cm, y2 = g(2t1)

2 = 4y1

= 4(10 cm) = 40 cm, y3 = g(3t1)2 = 9y1 = 9(10 cm) = 90 cm, etc. This spacing gives about

a 0.143 s interval between hits for uniformly accelerated motion.

The weights of string B are evenly spaced and do not give equal time intervals as can be

shown using 2 i

i

yt

g. The times get progressively smaller.

EXPERIMENT 6. THE ADDITION AND RESOLUTION OF VECTORS:

THE FORCE TABLE

Problem in Kinematics (Can 1 = 2?)

This is similar to the Problem in Math Analysis demonstration in Experiment 4 but involves

kinematics. In applying kinematic equations, it is important that we know certain

restrictions, as the following shows.

A student trying to solve a problem with constant acceleration wants to find the velocity, v.

The student is given that vo = 0 but is not given the acceleration a. Looking at the list of

kinematic equations, he decides to use v = at and x= a/t2 (with xo = 0 and vo = 0) so that

the unknown a can be eliminated. Then equating the a

2

2v x

t t

But x is not known, so he decides to use x = vt to eliminate it, and

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2

2v vt

t t

Simplifying,

v = 2v or 1 = 2!

Explanation

The equation v = at applies only to nonaccelerated motion and hence does not apply to the

problem.

ATWOOD MACHINE

Which Way Does The Bubble Go? (Mass and inertia)

The action (or inaction) of inertia may be demonstrated using a small level. When the level

is given a push, which way will the horizontal bubble go?

Item needed

Small level with horizontal tube

Procedure

1. With the level resting on a table, prepare to give it a push. Ask the students which

way the bubble will go when the push (a force) is applied, and the level is

accelerated.

2. Give the level a gentle push. The bubble goes toward the front of the level or in the

direction of the motion. Many students will guess otherwise. Ask for an explanation.

Explanation

Students guess that the bubble will move toward the back of the level because we are used

to observing the bubble instead of the liquid. The bubble is chiefly air, which little mass or

moves towards the front of the level. Because of inertia, the liquid resists motion and "piles

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up" toward the rear of the level, forcing the bubble forward. Think about giving a stationary

pan of water on a table or push. What happens to the water?

EXPERIMENT 8. CONSERVATION OF LINEAR MOMENTUM

-and-out)

five suspended identical metal balls.

When one ball swings in, after multiple collisions, one ball swings out at the other end of

the row of balls. When two balls swing in, two swing out; when three swing in, three swing

out, and so on always the same number out as in (even when five swing in).

Note that the initial potential energy (mgh) is conserved the final height(s) of the outgoing

balls is essentially the same as the initial release height(s). This means that kinetic energy is

conserved during the collision process. The collisions are therefore elastic conservation of

momentum and kinetic energy. This fact is used in the experiment demonstration, which

asks students if two balls swing in with a velocity v

velocity of 2v?

Item needed

Explanation

The collisions along the horizontal row of balls are approximately elastic. If two balls

conservation of momentum: 2 2 .m v m v However, another condition applies for elastic

collisions

for this case.

If iK is before and fK is after,

i f

2?21 12 2

2 2

2 2

2

K K

m v m v

mv mv

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Hence, the kinetic energy would not be conserved if this happened, and the equation tells us

that this situation violates established physical principles and does not occur. Note that

more energy out than in.

EXPERIMENT 9. PROJECTILE MOTION: THE BALLISTIC PENDULUM

Pendulum and Peg (Conservation of energy)

A pendulum and peg is used to demonstrate the conservation of mechanical energy.

Items needed

Pendulum and peg setup as shown below. (A pendulum suspended from the top of a

doorway and a broom handle across the doorway works nicely.)

Procedure

Point out to the students how the pendulum bob rises to the same height on both sides of the

swing when allowed to swing freely. Ask the students what will happen if the string of the

swinging pendulum hits a peg, interrupting the swing. Interrupt the swing of the pendulum

with the peg and demonstrate that the pendulum bob still rises to the same height.

Explanation

The kinetic energy gained on the downward swing is converted to potential energy as the

bob rises after hitting the peg. With mechanical energy conserved, the bob rises to the same

final height (with negligible energy lost in the string-peg collision).

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EXPERIMENT 10. CENTRIPETAL FORCE

Bucket Swing (What keeps the water in the pail?)

This demonstration illustrates the concept of centripetal force and acceleration. A bucket of

water is swung in a vertical circle with the water staying in the bucket at the top of the

swing.

Items needed

Small bucket or pail with handle

Water

Procedure

1. Fill bucket to about full (to prevent splashing) with water.

2. Make sure you have plenty of free space, and swing the bucket back and forth

increasing arcs to gain momentum. Finally, swing the bucket in one or more

complete vertical circles, noting the water does not fall out at the top of the swing.

Explanation

Due to gravity, the water would certainly fall out of the upside-down bucket if it were

stopped at the top of the swing. Even when the moving bucket is at the top of the swing, the

water still falls with an acceleration g

on the bucket supplies a centripetal acceleration of at least g. Swinging too slowly to

achieve this acceleration may be a wet experience.

Sideline: The centripetal force of our orbiting Moon is supplied by gravity, and the Moon is

fly off tangentially from its orbit.

EXPERIMENT 12. WORK AND ENERGY

Two Ball Bounce (Energy transfer)

Energy loss and energy transfer is demonstrated by dropping balls.

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Items needed

Basketball and tennis ball or racquetball

Meter stick

Procedure

1. Individually drop each ball from shoulder height and observe the height each time

the balls bounce back, which will be to an increasingly shorter height. Energy is

lost. Where did it go? The fraction of initial potential energy (PE) lost may be

approximated by the ratio of the final height (hf) to the initial height (hi); that is,

final PE/initial PE = mghf/mghi = hf/hi.

2. Place the smaller ball on top of the basketball and drop them simultaneously from

shoulder height. (A small plastic or rubber ring may be placed on top of the

basketball to balance the smaller ball.) After hitting the floor, the basketball

rebounds to a lesser height than when dropped alone, and the smaller ball bounces

much higher. Why the difference in heights? (The initial and final potential energies

of the balls may again be approximated from the heights.)

Explanation

When dropped individually, potential energy is converted into kinetic energy, and upon

hitting the floor (h = 0), some of the kinetic energy is transferred to the floor and converted

to sound and heat.

When the two balls are dropped together and the basketball collides with the floor, some

energy is transferred to the floor as before. As the basketball rebounds with the remainder

of its energy, it transfers some energy to the smaller ball. Having less rebound energy than

when dropped alone, the basketball rebounds to a lesser height. The energy transferred to

the smaller ball causes it to rebound to a much greater height. This is because the smaller

ball weighs much less than the basketball and bounces much higher with the additional

energy.

15


EXPERIMENT 13. POTENTIAL OF ENERGY OF A SPRING

The Slinky Slinky (Why doesn't it fall?)

When dropped, a vertically extended Slinky seems to defy gravity.

Item needed

Toy Slinky

Procedure

1. Stand on top of a lecture table and hold one end of a Slinky, allowing the coil to hang

stretched toward the floor.

2. Release the Slinky and observe the bottom coils. The bottom end remains virtually at rest

until the entire coil has collapsed and then accelerates downward.

Explanation

When you let the Slinky go, the bottom of the coil remains at rest until the rest of the coil

has collapsed downward on top of itgiving the appearance of the bottom hovering in mid-

air. When you hold the Slinky dangling, gravity is acting downward on the bottom, and the

coil tension is acting upward (equal and opposite forces). When you drop the Slinky, there

is no motion of the bottom until it gets information that the tension is changing, so to speak.

This takes time. Essentially, a compression wave travels to the bottom, and the bottom coils

become aware that the Slinky has been dropped.

EXPERIMENT 14. TORQUE, EQUILIBRIUM, AND CENTER OF

GRAVITY

Which Way Does the Yo-Yo Roll? (Torque - rotational motion)

In a demonstration of torque, a string of a yo-yo resting on a level surface is pulled as

shown in the figure. Which way will the yo-yo roll?

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Item needed

Large yo-yo. [A demonstration yo-yo maybe constructed using two plastic plates (or

aluminum disks) and a large wooden spindle so the demo may be more easily seen.]

Procedure

Prepare to apply a horizontal force as shown above. Ask the students which way the yo-yo

will roll. Many will say away from the pull force, but it rolls in the direction of the applied

force (or to the right in the figure).

Explanation

The yo-yo rolls in the direction of the force because of the applied torque. Note that the

instantaneous axis of rotation is along the line of contact the yo-yo makes with the surface.

The movement or lever arm (r) is from the surface to the bottom of the spindle. If you were

to hold a stick standing vertically in place of this r vector and pulled on a string attached to

the top of the stick in the direction of the force, which way would the stick rotate? Of

course it would rotate clockwise (about the instantaneous axis of rotation). The yo-yo reacts

similarly, that is, it rolls in the direction of the pull.

Another interesting demonstration with the yo-yo is to pull the string upward at an angle to

the horizontal. As the angle is increased, the yo-yo's roll slows, until a critical angle is

reached, and the yo-yo does not roll. Increasing the pull angle to greater than the critical

angle causes the yo-yo to roll away or the left.

17


Candle Seesaw (Torque and equilibrium)

A drip candle with a needle through the middle is balanced on two objects. When both ends

of the candle are lit, it rocks up and down like a seesaw.

Items needed

Long drip candle

Needle

Pair of drinking glasses or beakers of the same height

Knife and pliers (or tweezers)

Procedure

1. Candle preparation: Expose the candle wick at both ends. Cut off the tapered end of

the candle so the length is relatively uniformly circular, leaving a small portion of

wick exposed. At the bottom, cut away the wax so the end of the wick is exposed.

2. Push the needle through the candle at about mid length. (Estimate or measure with a

ruler.) If the candle's wax is soft, you may be able to push the needle through with

the fingers. However, if the wax is too hard, hold the needle with the pliers and heat

it with a flame. The hot needle should be easy to push through the wax at the

midpoint.

3. Balance the needle between two glasses. The candle may dip slightly if not evenly

balanced, but this is no problem.

4. Light both ends of the candle and observe it rocks up and down as the wicks burn.

Explanation

The candle rocks up and down because of unbalanced torques. A heavier end is tilted

downward, wax melts and drips off, making the end lighter. The other end is now heavier

and has greater torque, which rotates (rocks) the candle in the opposite direction. The

process is continuously repeated.

brium)

A straight-back chair sits against a wall. From equal positions, a female student can pick up

the chair, but a male student cannot.

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Items needed

Sturdy straight-back chair.

Procedure

Place the chair with its back against a wall. The female student stands next to the chair with

toes touching the wall, then takes two foot-steps backwards. (That is, bring the toe of one

foot behind the heel of the other foot twice and end up with the feet together, away from the

wall.) Next, leaning forward and place the head against the wall, reach over to bring the

chair directly in front, and place one hand on each side of the chair seat. Finally, without

moving the feet, stand up while lifting the chair. Most female students can do this, but

males will generally not be able to.

Explanation When a male student bends over and tries to lift the chair, he is in unstable

equilibrium (but fortunately using his head he doesn't fall over). That is, the center of

gravity of the male student/chair system falls outside of (in front of) the system's base of

support -- his feet. Males tend to have a higher center of gravity (larger shoulders and

narrower pelvis) than do females (narrow shoulders and larger pelvis). As a result, the

center of gravity of the female student/chair falls inside the feet base of support. She is in

stable equilibrium and so is able to stand from the bent position while lifting the chair.

But wait! The male student applies physics and swings the chair back behind him. The

combined center of gravity is now over his base of support, and he can stand while holding

the chair.

*Stack Them Up (center of mass - equilibrium)

Overlapping books are stacked on top of each other on the edge of a table until the stack

topples, showing the location of the center of gravity (mass) in stable and unstable

equilibrium.

Items needed

lab to use.)

19


Procedure

1. Place one book on a table with the short side of the book even with the table edge.

(Length of book on the table.)

2. Place another book on top of the first with 6.0 cm extended over the edge of the

short edge of the book and table. Ask the students to estimate how many books they

think can be placed in this manner before the stack topples.

3. Continue to stack books with 6.0 cm extending over the book beneath noting the

number of stacked books.

4. How were the estimates and why did the stack fall?

Explanation

As the books are stacked the center of gravity of the stack moves away from the table. For

example, let's take the length of a book to be 30 cm. The center of gravity (cg) of the first

book on the table is at the center or 15 cm from the edge of the table, which is taken as the

zero reference point for the locations of the cg's of the stacked books. Then the location of

the center of mass (or center of gravity) for the first two books (of equal mass) is given by:

1 2CM

0 6.0 cm3.0 cm

2 2 2

ix x xX

where x is the distance of each book's cg from the zero reference point.

So the cg of the two book stack is 3.0 cm toward the edge of the table from the zero

reference point (center of first book, x1 = 0). Repeating this for each additional book, the cg

of the stack moves 3.0 cm for each added book. Then, with 3.0 cm displacement for each

added book, it would take 3.0 cm x 5 added books = 15 cm to move the location of the

stack cg over the table edge in unstable equilibrium. (Six stacked books in total counting

the bottom one.)

The stack may not topple if the sixth book is positioned very carefully, but a seventh

book would definitely cause the stack to topple.

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EXPERIMENT 15 SIMPLE HARMONIC MOTION

*Cylinder Derby (rotational motion and moment of inertia)

Solid and hollow cylinders of different sizes are rolled down an inclined plane. Which rolls

faster? The characteristics of mass an size are investigated.

Items needed

Several solid and hollow cylinders of different sizes. (Food cans make good solid

cylinders, and cans with the food removed and end cut off are hollow cylinders, as

are napkin rings, etc.) Keep in mind that this is a rigid body demonstration. Cans of

juice, soda, and soups aren't rigid bodies.

Inclined plane

Scales and ruler

Timer or stopwatch

Procedure

1. Release various pairs of one solid cylinder and one hollow cylinder simultaneous

from the top of the inclined plane. Note which cylinder reaches the bottom first.

Then time the roll time of each and record. Also, try races with pairs of two solid

and two hollow cylinders.

2. Weigh the cans to determine the masses and measure the radii. Comparing the race

pairs, see if any connection can be made to which rolls the faster or slower.

Explanation

Rotational motion depends on the moment of inertia, 2i iI m r , which is constant for a

rigid body. I is a measure of rotational inertia, or a body's tendency to resist changes in its

rotational motion. The moment of inertia depends on mass (m) and distribution of particles

(r i). In general, the moment of inertia is larger the farther the mass is from the axis of

rotation. How does this relate to the cylinder races?

21


*Egg Spin (rigid body rotation)

Place an egg on a table and give it a sharp spin. A raw egg will move and wobble a bit, but

a hardboiled egg will spin and rise up on its end.

Items needed

Raw and hardboiled eggs (It is helpful to have several eggs of each kind in case of a

spinning accident.)

Procedure

How does one tell a raw egg from a hardboiled one (without cracking)? Easily. Place an

egg on a table and give it a sharp, quick spin. If raw, the egg will not spin. If hardboiled, the

egg will spin; and if given enough initial torque, will rise up on its end.

Explanation

Rotational motion is characteristic of a rigid body, which is an object in which the distances

between the particles are fixed (remain constant). A hardboiled egg is a rigid body, and

hence will rotate. A raw egg is not, and the particles inside can move relative to each other.

When trying to spin a raw egg, the inside material moves (slouches around so to speak) and

the egg will not spin.

Supplement

If you would like to demonstrate the concept of a rigid body, boil several eggs (half dozen

or so), removing one every minute or 30 seconds of boil. (It is best to experiment with the

time as eggs have different sizes.) After cooling, try spinning the eggs versus boil time until

one is found that spins. Then crack the eggs open starting with the least boiled and examine

the insides. Are they rigid bodies?

EXPERIMENT 17 STANDING WAVES IN A STRING

*Transverse and Longitudinal Waves (vibrating and singing rod)

An aluminum (Al) rod can be used to demonstrate transverse and longitudinal vibrations.

When held properly with the fingers and struck with the hand, the rod will vibrate

22


transversely and a wave form observed. Again hold the rod with the fingers and stroking the

rod, longitudinal waves may be set up which are heard as sound.

Items needed

Al rod, 1.3 cm diameter, about 2 m long. (Usually available from hardware stores.

Rod sets may be commercially available.)

spray)

Marker

Steel wool

Rod preparation

Transverse: Mark rod at center and at points 0.776 and 0.224 times its length.

Longitudinal: Mark rod at center and at points 1/4 and 1/6 of way from one end.

Procedure (practice helps)

1. Transverse mode: hold rod between the thumb and forefinger at one of the outer

points and strike the rod sharply with the hand at the center point. This will produce

a standing wave with nodes at the outer marked points. Use a finger of the free hand

to support the rod at the other outer point to hold the rod horizontally so the

vibrating ends may be better seen.

This fundamental frequency corresponds to that of an open organ pipe.

2. Longitudinal mode: Hold the rod with the thumb and forefinger at the center point.

With powdered rosin fingers of the other hand, pinch and firmly stroke the rod until

sound is produced. This may take practice and the fingers should not slip. (If the

rod has not been used for some time, it may be necessary to clean the rod with steel

wool.)

Note: with the singing rod held horizontally and rotated back and forth, the

Doppler effect can be heard.

3. Repeat Procedure 2 holding the rod at each of the other marked points. Higher

frequencies (pitches) will be heard.

23


Explanation

Transverse mode: Your finger and thumb are at one of the nodal points for the second

harmonic (analogous to the second harmonic of an open organ pipe). Holding the rod

horizontally has the finger at the other nodal point.

Longitudinal mode: The finger and thumb are holding the rod at the center node of the first

harmonic. Holding at the point closest to the center is at a node for the second harmonic and

at the point closest to the end the third harmonic

*Musical Straws (make your own kind of music)

A plastic drinking straw can be made to resonate with sound when properly prepared. Then,

using two straws or cutting the resonant straw, the effect of air column length on harmonics

may be demonstrated.

Items needed

Plastic drinking straws of two different diameters, with one straw fitting in the

other. (Different diameter straws are generally available at different fast-food

restaurants.)

Sharp scissors

Procedure

1. Chew 1 1.5 cm of one end of the larger diameter straw so as to make it flatter and

somewhat flexible. (Chewing with the back molars is usually best.)

2.

the end (the shape of a spear). The chewed portion should extend slightly beyond

chewing. In either

3. Place this end of the straw in your mouth with the lips firmly on the round portion

of the straw and blow. With a little practice, the straw will resonate with sound.

4. Put the smaller diameter straw inside the chewed straw and blow to sound the straw

again. Move the inner straw back and forth (trombone style) to show how the

resonant frequency varies with length. (A straw kazoo.)

24


5. Remove the inner straw and prepare to sound the chewed straw with scissors in

hand. While blowing into the straw and producing sound, use the scissors to cut

about an inch off the straw, then quickly another inch. and another until you get

close to your li

varies with length. If you make several cuts while continuously blowing in the

straw, it sounds like you are running a musical scale.

Explanation

Single straw: The chewed end of the straw acts like a reed to set up vibrations as in musical

instruments.

Double straws: The fundamental frequencies of a pipe (straw) varies inversely as the length

of the pipe. 1 1,2,3,...

2n

vf n nf n

L

Cut straw: Again the frequency varies with inverse length the shorter the straw, the higher

the frequency.

*Singing Wine Glass (resonance)

A crystal wine glass can be made to resonate (sing) with a loud sound with a finger driving

force.

Items needed

Crystal wine glass or brandy snifter. (A thin wine glass made of regular glass will

sometimes resonate, but crystal glass is better.)

Procedure

1. Wet your finger with water, and hold the base of the glass firmly on a counter or

table with the other hand. Carefully run the wet finger around the rim of the glass. A

slight pressure may need to be applied. When done properly, you will a sound or the

glass will "sing."

2. Put some water in the glass so it is about one-quarter full. Repeat the above

procedure. Note any difference in the sound.

25


3. Add more water to the glass and repeat. Do this for 2 or 3 water level. When the

glass is almost full, note the vibrations in the water around the sides of the glass.

Explanation

When driven with the finger, the glass vibrates at its resonant frequency. (The glass acts as

a closed pipe.) The empty glass resonates at its natural frequency. Adding water for

different levels (pipe lengths) gives overtones.

*Whirly Tube (Bloogle resonator)

A flexible corrugated plastic tube is swung around to produce resonant frequencies of the

tube.

Items needed

Whirly tube or Bloogle resonator. (Commercially available. Bilge pipe, from a marine

store, also works nicely and can be obtained in various lengths.)

Procedure

Hold the tube by one end and whirl (swing) it around in front or overhead to produce

resonant frequencies of the tube. Keep both ends of the tube open for the free flow of air.

Increasing the speed of rotation raises the frequency of the harmonic.

Explanation

Standing wave resonances are produced in the tube. The velocity at one end of the tube

causes air to flow in by the Bernoulli effect. The corrugated ribs causes the air flow to

vibrate. Increasing the speed of rotation produces increasing overtones. The length of the

tube determines the number of harmonics. The fundamental frequency can be produced by

blowing into one end of the tube.

26


EXPERIMENT 18 TEMPERATURE AND THERMOMETER

CALIBRATION

*Burning Dollar Bill (money to burn)

A dollar bill is immersed in a flammable liquid and then held up and set on fire. There is a

bright flame, but the bill is not consumed.

Items needed

Dollar bill (Borrow one from someone to make the demo more dramatic... maybe

even a $5 or $10 bill.)

50-50 mixture of rubbing alcohol (70% isopropyl) and water

metal tongs (to hold bill)

matches

Procedure

1. Immerse bill in the liquid and hold up by one end with tongs to drain.

2. Hold a match at the bottom of the bill and light. Flame will engulf the bill but it is

not singed.

Explanation

The alcohol-water mixture quickly burns but does not produce enough heat to provide the

ignition temperature of the bill.

EXPERIMENT 19 THE THERMAL COEFFICIENT OF EXPANSION

* Drinking Bird Engine (Perpetual motion?)

. heat is

continually converted into mechanical work.

Items needed

Drinking bird (available commercially)

Beaker or glass for water

27


Procedure

Set up the bird so its beak will pivot into the water container. To start the engine,

completely wet the absorbent flock on the head and beak and allow the bird to stand

upright. In a short time, it will pitch forward to wet the beak and then rise up. This will be

repeated over and over without assistance.

Explanation

Inside the body of the bird is a highly volatile liquid, such as ether, which has a low boiling

point and readily vaporizes at room temperature (heat supply). The evaporation of the

volatile liquid in the lower part of the body (bulb) creates pressure above the liquid. The

liquid in the tube does not evaporate as readily because the head is cooled by evaporation of

water from the flock material, and there is less pressure in the head. The pressure difference

causes the liquid to be forced up the tube into the head.

The rising liquid raises the center of gravity of the bird above the pivot point, and it pitches

body are equalized, and the liquid drains back into the body. The bird pivots back and the

cycle begins again.

*Salt and Ice: Melting and Freezing (M elting and freezing)

Salt is known to cause ice to melt. This is demonstrated by putting salt on a wet string on an

ice cube. But, there is refreezing as evidence by picking up the ice cube wih the string.

Items needed

Piece of string

Ice cube

Salt

Procedure

1. Wet the string thoroughly and lay it across the ice cube.

2. Sprinkle salt along the line of the string on the ice.

3. In several minutes, pick up the ice cube by the string.

28


Questions

Students may be assigned to do a paper on these questions.

1.

so.

2. Why did the ice cube freeze on the string?

Explanation

Salt (sodium chloride, NaCl) melts ice provided there is some liquid water present. Ice is

typically coated with a thin film of water, which is adequate. (Here the string is quite wet.)

Ice melts essentially because adding salt lowers the freezing point of the water. It does so

by affecting the normal phase equilibrium, which has as many molecules melting as

refreezing. When salt is added to water, salt molecules are dissolved into the water, and the

freezing point becomes lower as more molecules dissolve. Normally, as on a sidewalk, salt

can melt ice down to a freezing point of about -9 oC (15

oF).

The melted salt water is in contact with the ice cube (at 0 oC or 32

oF) and its temperature is

quickly lower below its freezing point and quickly refreezes, allowing the ice cube to be

picked up by the string.

oF,

and salt is applied, nothing happens other than coating the ice with salt. On the other hand,

if you put salt on ice at 15 oF or above, the salt will be able to prevent the melting ice from

2) lowers the

freezing point to about -15 oC (5

oF) and calcium chloride (CaCl2) to about

-29 oC (-20

oF).

EXPERIMENT 20 SPECIFIC HEAT

*Take the Heat (Specific heat)

The different absorptions of heat (specific heats) by two liquids in styrofoam cups is

demonstrated.

Items needed

29


Three Styrofoam cups

Vegetable oil

Water

Candle

Two small graduated cylinders or beakers

Timer or stopwatch

Procedure

1. Measure equal volumes (30 40 mL) of oil and water in the cylinders. Noting the

volumes are equal, pour into Styrofoam cups. (The volume may be varied,

depending on the size of the cup. Have about 1 cm depth in the bottom of the cup.)

2. Light the candle and hold the empty cup over the flame to show how quickly it

melts a hole.

3. Hold the cup with the oil and start the timer. Have the flame close to the bottom of

the cup, but not touching. Move the cup around so as to heat the bottom evenly.

Note the time when a hole is burned in the cup. (This is best done over a sink or

container to catch the oil. It may be convenient to place the cup in a tall ring stand

and move the candle so the heating effect can be better seen.)

4. Repeat procedure 3 with the water cup.

5. Note the difference in the times and explain.

Explanation

The water time should be considerably longer because of the higher specific heat, the heat

(transfer) required to raise the temperature of 1 kg of a substance by 1oC. That is, the

greater the specific heat, the greater heat capacity and more heat can be absorbed for a

temperature increase. The specific heat of water is 1.0 J/(kg - oC), and the specific heat of

vegetable oil is 0.4 J/(kg - oC).

30


EXPERIMENT 21 A

DENSITY

*Poke a Hole (and no water from bag)

The demonstration consists of pushing wooden pencils completely through both sides of a

plastic bag filled with water and none leaks.

Items Needed

Quart-size plastic bag with zip lock

Four round wooden pencils

Water

Paper towels (in case needed)

Procedure

1. Sharpen the pencils to very sharp points.

2. Fill the plastic bag 2/3 to 3/4-full of water and zip.

3. Ask the students if they believe you can push the pencils through both sides of the

bag and not lose any water.

4. Holding the top of the bag in one hand, place a pencil tip on the bag about the mid-

water line. Firmly and steadily push the pencil through one side of the bag. Then

continue pushing the pencil through the other side of the bag. (Portions of the pencil

should extend from both sides of the bag and no water loss.)

5. Repeat with the other pencils at different locations and angles.

6. When finished, hold the bag over a sink and remove the pencils showing the water

flows out the holes. The students may want to inspect the bag and pencils.

Explanation

Plastic bags are made of long-chain polymer molecules. When the bag is punctured by a

pencil, the long-chains form a seal around it and prevent leakage.

31


EXPERIMENT 22 FIELDS AND EQUIPOTENTIALS

*Electrostatics in Action (L evitation)

A demonstration of electrostatic repulsion (the law of charges) by levitating a thin plastic

loop. (Supplement following Explanation gives other electrostatic demonstrations.)

Items needed

Balloon

Plastic produce bag (found in produce section in grocery stores)

Scissors

Cotton towel

Procedure

1. With the scissors, cut a 1.5 inch strip from the open end of the plastic bag. (The end

that is usually hard to get open.) Open the strip so you have a thin circular ring or

loop.

2. Blow up the balloon and tie the end.

3. Rub the towel over the surface of the balloon for 15-30 seconds. (Time may depend

on humidity.)

4. Lay the plastic loop on a flat surface, and holding one end rub the towel on the loop

for 15-20 seconds. Turn over the loop and repeat so that both sides are rubbed.

5. Hold the unfolded loop 6-

while moving the balloon under it. (The loop may stick to your hand but shake it

loose.)

Explanation

Rubbing the towel against the balloon and plastic loop leaves both objects negatively

charged (charging by friction). The loop floats or levitates above the balloon because of the

law of charges (like charges repel).

Supplement

Additional electrostatic demonstrations:

32


fine hair). Separate and the hair stands up and is

attracted to the balloon. (Charging by friction, object oppositely charged and attract.)

* Charging by induction (induced molecular dipoles)

Bring a negatively charged balloon near small pieces of paper on a table. Small bits

of paper are attracted and cling to the balloon. Paper molecules are polarized with

definite regions of charge, giving rise to a net attractive force.

Rub a balloon on sweater or hair, and it will stick to the wall or ceiling. Molecules

in the wall or ceiling materials are polarized, giving rise to a net attractive force.

Bring a negatively charged balloon near a very small stream of water from a spigot.

The stream will bend toward the balloon (polarized water molecules).

M AGNETIC DEM ONSTRATIONS

Note: the first of these demonstrations generally require strong neodymium (rare earth)

magnets. The final demo uses a standard (AlNiCo or ceramic) magnet. Caution: In using

strong magnets it is prudent to remove wrist watches, calculators, or cell phones from the

vicinity, as parts may become magnetized and inoperative.

*Magnetism Through the Hand

Demonstrates that magnetism (magnetic field) can penetrate flesh (a hand) without

obstruction.

Item needed

Several paper clips

Procedure

1. Lay the magnet on the back of the outstretched hand.

2. Position a paper clip touching the palm of the hand, which will be attracted.

3. See how many clips can be added individually to the first to form a descending

chain. (You may want to have a student contest.)

Explanation

Magnetic fields can penetrate nonferrous materials.

33


*Is Money Magnetic? (2 demos)

This question is inspected in two demonstrations.

DEMO 1. Dollar Bill

Show that a dollar bill will be attracted to a strong magnet.

Items needed

Procedure

1. Fold the bill at about 55-60% of its length. Lay the long end of the bill on a table so

that the folded shorter end stands up at an angle.

2. Bring the magnet close to the standing end of the bill, and it will be attracted and

move. Touching the magnet, it will stick. (As an alternative method, hold the bill

between the thumb and forefinger and bring the magnet close to the other end of the

vertical bill for similar effects.)

Explanation

The bill is magnetic because its ink contains iron oxide (ferrous oxide) and very small

particles of iron.

DEMO 2. Coins

Shows that some coins are magnetic.

Items needed

Neodymium magnet (A standard magnet may be used in this demo.)

Several U.S. and Canadian coins (nickels, dimes, or quarters)

Procedure

1. Show the collection of coins in your hand and ask if such money is magnetic.

(Generally, some students will say yes and some no.)

2. Having coins and magnet, apply the scientific method to find out.

34


3. Move the magnet around in the coins and lifting, some coins will stick (to the

delight of the "yes" students).

4. But wait, some coins aren't attracted. Why is this?

Explanation

The attracted coins are Canadian, which contain predominantly the element nickel (Ni), a

ferromagnetic material. The unattracted coins are U.S., which are primarily copper and

zinc, with only a relatively small amount of nickel.

*Eating Magnetic Iron for Breakfast (2 demos)

Two demos to show that some iron-fortified breakfast cereals contain enough iron to be

attracted by a magnet.

Items needed

Neodymium magnet

Flakes of an iron-fortified breakfast cereal (for example, Total or similar brand.

Check box Nutritional Facts for 100% iron.)

Spoon and plate (that will hold small level of water)

DEMO 1. Crumbs

Procedure

1. Put several flakes of cereal on the plate and crush with fingers. Then use spoon to

further crush into fine crumbs.

2. Bring the magnet close to the crumbs. Some should be attracted and move. Putting

the magnet in the crumbs and lifting, crumbs will stick to the magnet.

DEMO 2. Flakes

Procedure

1. In an empty plate, put a small amount of water, enough so several cereal flakes will

float when gently added.

2. Bring the magnet near a flake and move around. Flakes will follow the magnet.

35


Explanation

Iron (ferrous) oxide in the iron-fortified cereal is magnetic.

*Which Rod is Magnetic?

There are two metal rods similar in appearance, but one is a magnet and one is plain iron.

The rods will attract, but how can you tell which is the magnet and which is iron?

Items needed

Standard magnet

Iron rod (or bar) of similar size, shape, and appearance as the magnet. (The magnet

and the iron rod may be painted so as to look identical.)

Procedure

1. Allow the students to inspect the rods and note attraction. Which is which?

2. Designate one rod as A and the other B. Touch the end of A to the middle of B. If it

sticks, A is the magnet and B is iron. If it doesn't stick, then B is the magnet and A

is iron.

3. This procedure may be reversed as a check, starting with the end of B to the middle

of A.

Explanation

In the center of the magnet between the poles, the field outside is weak. Because of this, the

iron is only weakly attracted to the middle of the magnet (not enough to stick). However,

the ends of the magnet will be attracted to any part of the iron rod.

EXPERIMENT 30 REFLECTION AND REFRACTION

*Mirror Right -left Reversal and Nonreversal (2 demos)

It is well known that plane mirrors produce a right-left reversal. Using two mirrors, one can

see things nonreversed.

36


Items needed

Two rectangular plane mirrors

Tape

DEMO 1. Double mirror

Procedure

1. Set up two mirrors with their edges touching and at a right angle. Tape along the

touching edges of the mirrors so they will stand freely.

2. Look into the common edge of the mirrors so you see partial images of yourself in

both mirrors. (This is how people see you in the second mirror.) Try winking or

pulling your ear. Hold a printed page or a clock in front of the mirrors. Try

performing some simple tasks like parting and combing your hair, etc. and see how

you do.

DEMO 2. Single mirror symmetry

Procedure

1. Sometimes you can "fool" the right-left reversal. For example, using one mirror look at

the following word with the edge of the mirror at the right side of the word, and then with

the edge of the mirror above the word.

HOE

Try another with the mirror in both positions.

WEOM

Now try looking at the following word with the mirror held at the sides and above and

below.

WOW

(Have the students make up several nonreversing words of their own. Which letters can be

used? Consider and label only sideways nonreversals, and both sideways and top-bottom

reversals.)

37


Explanation

In Demo 1, the taped mirrors allow a double right-left reversal, which negates the observed

reversal. In Demo 2, certain letters of the alphabet exhibit symmetry such that they do not

appear to be right-left reversed.

It should be noted that the right-left reversal is really caused by a front-back reversal. For

example, standing in front of a mirror facing south, your back then "faces" north. However,

your image has its front facing north and its back to the south -- a front-back reversal. To

further demonstrate this, have one of your lab partners face you (no mirror). If your partner

raises his/her right hand, you can see that hand is actually on your left side.

*N efraction)

A glass stirrer is immersed into a clear liquid, and it disappears. Magic?

Items Needed

Pyrex glass stirring rod (from Chemistry dept.)

100% Mineral oil or vegetable oil

(Supplement) Glass gems (from a craft store)

Procedure

1. Pour oil into a clear, thin-walled glass. (A clear wine glass works well, or for greater

effect, use a cylinder to complete immerse the rod.)

2. Lower the rod into the liquid, and the section in the liquid will seemingly disappear.

If a cylinder is used so the rod is completely immersed, it disappears completely.

3. (Supplement) Glass gems may be put at the bottom of a glass and the oil added

they disappear. Did they dissolve? Inversely, the gems may be dropped into a glass

with oil.

Explanation

another, n1 1 = n2 2, where n is the index of refraction. When light passes through

38


law (as well as some reflection at the surfaces). Although an object is transparent, it is still

visible due to refraction (and reflection).

The reason the glass rod (and gems) seem to disappear is because the objects are index

matched. That is, the rod (and gems) have almost the same index of refraction as the oil. As

a result, there is little or no refraction (or reflection), and the glass objects appear almost

completely invisible.

EXPERIMENT 31 SPHERICAL MIRRORS AND LENSES

*Spherical Mirrors ( Upside down or right-side up?)

When you look into the front side of a shiny spoon, you will see an inverted image of

yourself. When you look into the back side of the spoon, you see your image upright. Why

is this? [You might check it out before lab when having breakfast (early lab) or lunch (late

lab). Try it at dinner if you have an evening lab.]

Item needed

Shiny tea, soup, or table spoon.

Procedure

Do as described above, and ask students why images are upright and inverted.

Explanation

This is like alternately looking at concave and convex mirrors. Looking into the front of the

spoon (or a concave mirror) as an object, you are inside the focal length, and the image is

inverted. As you move the spoon away from you, the inverted image becomes smaller.

(This may be shown with ray diagrams in your textbook.)

Looking at the back of the spoon (or a convex mirror), your image is upright as all images

are for convex mirrors.

39


The Scientific Method and Thought

COMMENTS AND HINTS

This experiment which is new to the 8th edition looks at physical measurement from a point

of view seldom seen in an elementary physics laboratory. It is really a study of people and

how they can be misled by their perceptions.

In part A, The Dollar Drop, we use the equation d = gt2 to calculate our reaction time and

show that our ability to time things is limited. b

their arm on the edge of a table or the back of a chair to prevent them from moving down as

they try to grab the bill. At this point you m

that in the absence of air resistance all objects fall at the same rate. There is the classic

demonstration consisting of a tiny feather and a penny sealed in a glass tube. When the air

is pumped out, the penny and feather fall at the same rate. But this demonstration is not

visible beyond about the second row of the class, and many schools do not have this

demonstration tube or the vacuum pump. There is a simpler way to do the demonstration

with a book and a feather. In the absence of a feather, a dollar bill will do. Simply hold the

book flat and place the feather on top of the book. When released the book brakes the wind

for the feather, and they fall together. The dollar bill is only 0.155 m long. Solving the

equation for t we have t d/g m)/(9.8m/s2)) = 0.18 seconds.

In part B, The Muffin Cup Drop, we look at the other extreme where air resistance can no

longer be neglected; in fact, it cancels out the force of gravity, and heavy objects do fall

faster. Aristotle was not wrong, but he was solving a different problem. The two special

cases are considered because they can be solved without using differential equations or

calculating it incrementally with hundreds or thousands of calculations.


40


Part C deals with optical illusions to show how our perceptions can be fooled, as well as the

importance of the role of instruments in the collection of experimental data.

ANSWERS TO EXPERIMEN T QUESTIONS

Questions

1. If you dropped the dollar bill (or ruler) yourself, how might this affect the reaction

time?

The reaction time is eliminated because both hands are triggered to move together.

2. Suppose 3 nested muffin cups and 5 nested cups were used in the experiment. From

what height should the 5 cups be dropped to hit the floor together with the 3 cups

dropped from a height 1 meter?

According to Equation 1.1 (d2/d1) = (m2/m1)1/2

or d2 = d1(m2/m1)1/2

Therefore: d5cups = d3cups(m5cups/m3cups)1/2

= 1.000 meter (5/3)1/2

= 1.291

3. Why are instruments so important in taking experimental data, rather than using our

senses directly?

As illustrated by Part C of this experiment, perception can be fooled. Instruments

are designed to be used in such a way that the readings are not influenced by

perception.

POST-LAB QUIZ QUESTIONS

Completion

1. Testing theoretical predictions against experimental results is the principle of the

scientific method.

2. A possible explanation of an observation is a hypothesis.

3. The testing of a hypothesis under controlled conditions is done by experiments.

4. If a hypothesis passes enough experimental tests and generates new predictions that also

prove correct, it becomes a theory.

41


Multiple Choice

1. Testing theoretical predictions against experimental results is called (a) first-order

approximation, (b) second-order approximation, (c) trial and error, *(d) the scientific

method.

2. A possible explanation of an observation is a (a) theory, *(b) hypothesis, (c) law, (d)

mistake.

3. If a hypothesis passes enough experimental tests and generates new predictions that also

prove correct, it becomes a *(a) theory, (b) rule, (c) law, (d) mistake.

Essay

1. Distinguish between a hypothesis, a theory, and a law.

42


Experimental Uncertainty (Error) and Data

Analysis

COMMENTS AND HINTS

This experiment is considered to be an important initial operation for students. The

principles will be applied in error and data analysis in following experiments.

(a) Because the sets of data taken in many of the following experiments have only

several values, they do not lend themselves to detailed statistical analysis. For this

reason, the section in this experiment on Standard Deviation is labeled as optional.

As the instructor, it is your option to include or omit this section. It is considered to

be instructive for most students to be at least introduced to statistical analysis. Of

course, your decision must be guided by the time for the laboratory and student

speed and skills as well as by the nature of your course (i.e., this section should

probably not be omitted for students of physics and engineering).

(b) Of particular importance is the section on Graphical Representation of Data. It has

been the experience of the author that students generally submit poor graphical

representations of data (i.e., they turn in lousy graphs). This is in the form of graphs

with unlabeled axes and omission of units, straight lines connecting data points

(Figure 1.6, Graph A) instead of smooth curves, etc. It is strongly recommended that

major emphasis be placed on proper graphing procedures. It is highly important that

individuals in science fields know how to graphically represent data properly and

how to interpret those graphs to acquire useful information.

A concept introduced here and used in various experiments is the reduction of

nonlinear functions to linear functions of the form y mx b so that they may be

plotted on Cartesian coordinates and the slope and intercept values determined. This


43


should be stressed. (An optional method of plotting exponential functions with

semilog and log-log graph paper is discussed in Appendix D of the lab manual.)

(c)

ease of calculations) and French curves. The latter may be shown as a demonstration

or used by the students in drawing curves if you have a sufficient quantity available.

(d) Although students should be encouraged to use calculators, the instructor should

remain aware that most students feel that if their calculator displays 7 or 8 digits,

then this is what should always be reported. This is often done without any regard

for the significant figures of the numbers used to make the calculation involved. The

section on significant figures should be emphasized with regard to instrument

limitations, etc. This concept is reiterated in Experiment 2.

Note: The answers to the questions comprise the laboratory report for this experiment.

ANSWERS TO CALCULATI ONS IN LABORATORY RE PORT

Least Count

Data table 1&2

Student answers will depend on the size of the object they are given to measure.

Student answers will depend on data

Significant Figures

DATA TABLE 3

0.524 35.28 10

15.1 26.00 10

1440 8.25 10

0.0254 41.00 10

83,900 92.70 10

(b) 112 34 410 156128 16 102 3. . . . . cm

(c) 31.39 cm/4.25 cm = 3.15 (no units)

44


1. Expressing Experimental Error

(a) Fractional error 0.0027

Percent error 0.27%

(b) Percent difference 2.4%

Percent error E1 1.6%

Percent error E2 0.82%

Percent error of mean 0.41%

(c) In the table, the determination of average deviation and standard deviation

presents a problem. Since the subtraction usually produces only one significant

figure, the results are good to only one figure. Since the significant-figure rule of

thumb breaks down at one figure, I tell my students that they should always

keep at least two. Also, rounding should not be done until the final result.

DATA TABLE 4

Purpose: To practice analyzing data.

Distance (m)

Time t

(s) y1 y2 y3 y4 y5 y d

t2

(s2)

0 0 0 0 0 0 0 0 0

0.50 1.0 1.4 1.1 1.4 1.5 1.28 0.18 0.25

0.75 2.6 3.2 2.8 2.5 3.1 2.84 0.25 0.56

1.00 4.8 4.4 5.1 4.7 4.8 4.76 0.17 1.00

1.25 8.2 7.9 7.5 8.1 7.4 7.82 0.30 1.56

(d) Student graph.

(e) Slope should be very close to 5.0, making g 10.

(f) Percent error based on student result in (e) above.

(g) k ( . )/( . )313 0400 7825 783 N m . . N/m

(h) The slope of the graph should measure about 146 s2/kg.

Slope T m k2 24/ /

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2

2 /146 = 0.27 N/m


1. Ruler #1 has a least count of 1 cm, making 1/10 cm the best that can be estimated by

eye. The black bar clearly extends to a point over half way between 3 and 4 cm. I would

accept answers of 3.6 or 3.7 cm from students. Ruler #2 has a least count of 0.5 cm. The

bar extends about 3/10th of the least count division beyond 3.5 cm, which works out to

be 3.65 cm, but there is a big uncertainty in that last digit, so much so that most would

say that it should not be written, or it should be reported as 3.65 0.03 cm. Ruler #3 has

a least count of 1 mm, and the scale can be read as 3.65 cm. Now the last digit is

significant since we can say the result is 3.65 0.01 cm.

2. Probably not. The last measurement was read to more decimal places.

3. The points would be widely spaced, but the cluster would be centered at the center of

the target. An extreme example would be a series of evenly spaced points around the

edge of the target.

4. Percent error is an indication of accuracy, but the scatter or precision of the data is not

indicated. Percent difference is an indication of precision since it shows the ability of

two measurements to give the same answer.

5. The measurement of a physical constant usually involves several individual

measurements and a calculation. The uncertainty in the form of a plus or minus for each

measurement would be determined considering the nature of the instrument used to

make the measurement. A range of possible values for the physical constant is then

found by repeating the calculation with the extreme values of each of the measurements.


Completion

1. Errors associated with the calibration and zeroing of measurement instruments or

techniques are called systematic errors.

2. Errors resulting from unknown and unpredictable variables in experimental situations

are called random errors.

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3. In general, the accuracy of an experimental value depends on systematic errors and the

precision on random errors.

4. If there is no decimal point in a number, the rightmost nonzero digit is the last

significant figure.

5. To avoid problems with zeros in significant figures, powers of 10 or scientific notation

may be used.

6. The number of significant figures in the result of a multiplication or division is equal to

the number of significant figures in the data with the least number of significant figures.

7. In general when a calculation involves several operations, rounding should be done only

at the end.

8. To express percent error, an accepted value must be known.

9. The average value of a set of measurements is sometimes called the mean value.

10. In the equation of a straight line, y ax b, the a is the slope of the line and b is the Y

intercept.

11. The slope of a straight line on a graph is the ratio y/ x.

12. For a straight line on a graph (y ax b), the X intercept (y 0) is given by b/a.

Multiple Choice

1. The type of error that is associated with the calibration and zeroing of measurement

instruments or techniques is (a) personal error, *(b) systematic error, (c) random error,

(d) mathematical error.

2. The type of error that is minimized by making a large number of measurements and

taking the mean value is (a) personal error, (b) systematic error, *(c) random error, (d)

mathematical error.

3. The type of error on which the precision of a measurement generally depends is (a)

personal error, (b) systematic error, *(c) random error, (d) incorrect significant figures

in calculations.

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4. When several numbers are multiplied or divided, the proper number of significant

figures in the answer is equal to the (a) significant figures of the number with the most,

*(b) significant figures of the number with the least, (c) sum of the significant figures

found in the data, (d) average number of significant figures found in the data.

5. When a calculation involves several steps, the result should be rounded (a) after each

step, (b) whenever the number of digits becomes large, *(c) only at the end, (d) never.

6. The correctness of an experimental measurement is expressed in terms of (a) significant

figures, *(b) accuracy, (c) precision, (d) personal error.

7. The comparison of two equally reliable experimental measurements is often expressed

in terms of *(a) percent difference, (b) percent error, (c) average or mean value, (d)

significant figures.

8. The average or mean value of an experimental set of data gives the best value when the

measurements involve only (a) personal error, (b) percent difference, (c) significant

figures, *(d) random error.

9. The Y axis of a Cartesian graph is called the (a) mean, (b) abscissa, *(c) ordinate, (d)

slope.

10. The plotting of two variables such as T versus generally means that the values are

plotted on the *(a) X axis, (b) ordinate axis, (c) slope, (d) Y axis.

11. Error bars on a graph give an indication of (a) units, (b) abscissa values, (c) accuracy,

*(d) precision.

12. The slope of a straight-line graph is given by the (a) X intercept, (b) Y intercept, *(c)

ratio of a particular ordinate difference and the corresponding abscissa difference, (d)

ratio of the maximum X-axis scale to the Y-axis scale.

Essay

1. Distinguish and explain the difference between straight-line graphs with positive slopes

and those with negative slopes.

2. What would cause a skew or shift of the maximum of a normal or Gaussian distribution

of experimental values?

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Measurement Instruments

(Mass, Volume, and Density)

COMMENTS AND HINTS

To introduce students to experimental measurements, we make length and mass

measurements in this experiment and compute the densities of various materials. The

concept of instrument scale least count is included, which further reinforces significant

figures (or digits) in measurements in particular, the estimated or doubtful figure.

Density computations give practice using significant figures in calculations. Students are

also introduced to the vernier caliper and micrometer, which are usually unfamiliar

measurement instruments. Student difficulties in this experiment generally arise from the

following:

(a) Reading a vernier scale. Should you wish to emphasize the convenience of the

metric system, try having them use the upper English vernier scale, but most wisely

after the students have learned the use of the lower metric scale.

(b) The double rotation of the micrometer thimble for a 0.01-mm spindle movement.

-

experiment has been found to be helpful.

(c) Unless you are very specific in your pre-lab discussion, you will often find that

many students use the displacement method to find the volumes of all objects

instead of just using it to find the volume of the irregularly shaped object as

instructed in Procedure 10.

(d)

to fill in the blanks without regard to procedure. This is a very good place for you to


49


emphasize the importance of following procedure for this and for subsequent

experiments.


1. The biggest source of error is probably the least count and the zero reading, particularly

on the single sheet measurements. The inconsistent compression of air spaces between

pages is another source of error.

2. The most important factors will depend on the equipment used. In general, the smaller

measurements like the diameter of the wire and the thickness of the sheet will give the

largest percent error. It also should be noted that the densities given in Tables are for

pure materials. The samples tested in the lab are probably alloys designed to give better

mechanical properties.

3. Air bubbles will add to the measured volume. It is a systematic error since it always

adds. This error will give an experimental density that is too low.

4. Use a sinker weight attached to the floating object by means of a string to immerse the

object. Note the cylinder reading with only the sinker immersed; then note the cylinder

reading with both the sinker and object immersed (see Experiment 22).

5. Given r 20 cm, t 0.50 mm 0.050 cm, and Al g/cm273. (Appendix Table Al);

2 2(0.050 cm) = 63 cm

3

3)(63 cm

3) = 1.7x10

2

6. Determine the density of the crown using the water displacement method of finding its

volume and compare it with the density of gold.

Note: Students who understand the experiment seem to have little difficulty with


Completion

1. If an instrument scale has a least count of 1 cm, it can be read to the nearest 0.1 cm

or 1 mm.

50


2. A vernier scale is useful in reading the fractional part of the least count.

3. A negative zero correction is added to measurement readings.

4. When two rotations are required to move a micrometer thimble through 1.0 mm, the

pitch of the micrometer screw is 0.5 mm.

5. The instrument most convenient for measuring the inner diameter of a ring would be

the vernier caliper.

6. The ratchet mechanism on a micrometer permits the jaw to be tightened on objects

with the same force.

7. Density provides a measure of the relative compactness of matter in substance.

8. The units of density are kg/m3 or g/cm3.

9. If two objects of different volume have the same mass, the larger object has a

smaller density.

10. In terms of density and volume, the mass of an object is given by m V (density

times volume).

Multiple Choice

1. The instrument in the experiment with the smallest least count was the (a) meter

stick, (b) vernier caliper, *(c) micrometer, (d) all were the same.

2. The diameter of a round pencil or pen is most conveniently measured with a (a)

meter stick, *(b) vernier caliper, (c) balance, (d) graduated cylinder.

3. Before making a measurement, it is always important to

mass, (b) least count, (c) length, *(d) zero correction.

4. The function of a vernier scale is to (a) increase the least count, *(b) assist in

accurately reading the fractional part of a scale division, (c) allow inner diameters

to be easily read, (d) avoid positive zero corrections.

5. The main scale of a micrometer is on the (a) anvil, (b) spindle, *(c) sleeve, (d)

thimble.

51


6. If a micrometer screw had a pitch of 1.0 mm and there were 50 divisions on the

thimble, then a thimble division corresponds to (a) 0.01 mm, *(b) 0.02 mm, (c)

0.05 mm, (d) 0.10 mm.

7. A piece of dust or foreign matter on the flat jaw surface of the anvil of a

micrometer could give rise to a (a) more accurate reading, *(b) positive zero

correction, (c) negative zero correction, (d) random error.

8. If object A had twice the mass and one-half the volume of object B, then the density

of A would be *(a) four times that of B, (b) twice that of B, (c) the same as that of

B, (d) one-half that of B.

9. A graduated cylinder has a linear length scale on its side calibrated in volume units

because (a) it is a vernier scale, (b) length and volume are the same, *(c) the cross-

sectional area of the cylinder is assumed to be uniform, (d) it allows for different

liquid densities.

10. An average density is obtained when (a) an object is irregularly shaped, (b)

significant figures are not used in calculations, (c) personal error is involved, *(d)

the object substance is not pure or homogeneous.

Essay

1. Explain how the number of significant figures in a measurement value depends on

the least count of the measuring instrument.

2. Discuss the use of a balance on the moon. Would it accurately determine mass?

3. Could a meter stick be equipped with a vernier sca

pre lab demos

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